Wavelet-based simulation of random processes from certain classes with given accuracy and reliability

Abstract

Abstract We consider stochastic processes Y ⁢ ( t ) {Y(t)} which can be represented as Y ⁢ ( t ) = ( X ⁢ ( t ) ) s {Y(t)=(X(t))^{s}} , s ∈ ℕ {s\in\mathbb{N}} , where X ⁢ ( t ) {X(t)} is a stationary strictly sub-Gaussian process, and build a wavelet-based model that simulates Y ⁢ ( t ) {Y(t)} with given accuracy and reliability in L p ⁢ ( [ 0 , T ] ) {L_{p}([0,T])} . A model for simulation with given accuracy and reliability in L p ⁢ ( [ 0 , T ] ) {L_{p}([0,T])} is also built for processes Z ⁢ ( t ) {Z(t)} which can be represented as Z ⁢ ( t ) = X 1 ⁢ ( t ) ⁢ X 2 ⁢ ( t ) {Z(t)=X_{1}(t)X_{2}(t)} , where X 1 ⁢ ( t ) {X_{1}(t)} and X 2 ⁢ ( t ) {X_{2}(t)} are independent stationary strictly sub-Gaussian processes.